Question

A metal ball of mass 'm' is put at the point A of a loop track and the vertical distance of A from the lower most point of track is 8 times the radius 'R' of the circular part. The linear velocity of ball when it rolls of the point B to a height 'R' in the circular track will be

• A. $[10gR{]}^{1/2}$
• B. $7{\left[\frac{gR}{10}\right]}^{1/2}$
• C. ${\left[\frac{7gR}{5}\right]}^{1/2}$
• D. $[5gR{]}^{1/2}$

Answer 1

The correct option is A $[10gR{]}^{1/2}$

Applying the conservation of energy at points A and B, we have
$mg\left(8R\right)=\frac{m{v}^2}{2}+\frac{1}{2}I{\omega }^2+mgR$
or $mg\left(8R\right)=\frac{m{v}^2}{2}+\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\left(\frac{v}{R}\right)}^2+mgR$
$=\frac{7}{10}m{v}^2+mgR$
$mg(8R-R)=\frac{7}{10}m{v}^2$
$[10gR{]}^{1/2}$